On Minimal Length Factorizations of Finite Groups

DOI10.1080/10586458.2003.10504708zbMath1047.94014OpenAlexW1983860602WikidataQ114099364 ScholiaQ114099364MaRDI QIDQ4811487

Martin Roetteler, Rainer Steinwandt, María Isabel González Vasco

Publication date: 6 September 2004

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1064858780

zbMATH Keywords

simple groupsgroup factorizationsLogarithmic signatures

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Simple groups (20E32) Cryptography (94A60) Authentication, digital signatures and secret sharing (94A62) Products of subgroups of abstract finite groups (20D40)

Related Items (14)

Minimal logarithmic signatures for one type of classical groups ⋮ On the size of complete decompositions of finite cyclic groups ⋮ Complete factorizations of finite abelian groups ⋮ The existence of minimal logarithmic signatures for the sporadic Suzuki and simple Suzuki groups ⋮ Minimal logarithmic signatures for the unitary group \(U_n(q)\) ⋮ The Existence of Minimal Logarithmic Signatures for Some Finite Simple Groups ⋮ On Minimal Factorisations of Sporadic Groups ⋮ Minimal logarithmic signatures for classical groups ⋮ Minimal logarithmic signatures for finite groups of Lie type ⋮ All exceptional groups of Lie type have minimal logarithmic signatures ⋮ Exact Factorizations of Sporadic Simple Groups ⋮ The existence of minimal logarithmic signatures for some finite simple unitary groups ⋮ Factoring nonabelian finite groups into two subsets ⋮ Classifying exact factorizations of minimal length of sporadic simple groups

Uses Software

• GAP
• Magma

Cites Work

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• Algebraic properties of cryptosystem PGM
• On products of Sylow subgroups in finite groups
• The Magma algebra system. I: The user language
• New approaches to designing public key cryptosystems using one-way functions and trapdoors in finite groups
• The maximal factorizations of the finite simple groups and their automorphism groups
• Galois theory on the line in nonzero characteristic

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